So, in another thread about the Citation X, the fact that the Dassault Falcon 2000 has strange wings gets raised. It seems that, when on the ground, the wings are slanted down from the roots. I thought that such a configuration was really unstable, so why would they use it on a bizjet?

Manzoori is correct, the wings are usually seen bent down because of the fuel weight and their own weight. When in flight, the aircraft is literally lifted by the wings, so they can be seen bended upwards.

A fully loaded 747 shows its wings bent down while in the ground noticeably. This picture of a 747 just prior to t/o shows it a bit:

All other things being equal you should have more tendency to continue to roll with antihedral, that is why high wing transports use it, since their cargo is carried below the wing (C-5, AN-124) so it acts like a pendulum.

Actually the Tu-154 wing is one of the more flexible ones. The wing can be bent so that the tip is 14 meters from its original point before the wing breaks. Of course that doesn't happen in flight. The reason for flexibility is comfort because the flexible wing absorbs turbulence and also contributes to a very light touchdown. I'm guessing that the wing-mounted engines have something to do with the western aircrafts' wings bending more.